Abney says that it isn’t possible on every track in the game, some trees just don’t allow themselves to be removed. But there is always a chance at a perfect run, all you need is 3 stars in a row. Which, if you fall to 8th place immediately, he estimates will give you a 1 in 186th chance at in every run.
You can watch some of his “no tree” speed runs on his twitch channel, abney317.
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